A hemispherical bowl of internal radius $$\(6 r\)$$ is fixed with its circular rim horizontal. The centre of the circular rim is $$\(O\)$$ and the point $$\(A\)$$ on the surface of the bowl is vertically below $$\(O\)$$. A particle $$\(P\)$$ moves in a horizontal circle, with centre $$\(C\)$$, on the smooth inner surface of the bowl. The particle moves with constant angular speed $$\(\sqrt{\frac{g}{4 r}}\)$$. The point $$\(C\)$$ lies on $$\(O A\)$$, as shown in Figure 1. Find, in terms of $$\(r\)$$, the distance $$\(O C\)$$ (9)

Answer:

Knowledge points:

Solution: